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Magic Hexagon
A magic hexagon of order ''n'' is an arrangement of numbers in a centered hexagonal pattern with ''n'' cells on each edge, in such a way that the numbers in each row, in all three directions, sum to the same magic constant ''M''. A normal magic hexagon contains the consecutive integers from 1 to 3''n''2 − 3''n'' + 1. It turns out that normal magic hexagons exist only for ''n'' = 1 (which is trivial, as it is composed of only 1 cell) and ''n'' = 3. Moreover, the solution of order 3 is essentially unique. Meng also gave a less intricate constructive proof.Meng, F"Research into the Order 3 Magic Hexagon" '' Shing-Tung Yau Awards'', October 2008. Retrieved on 2009-12-16. The order-3 magic hexagon has been published many times as a 'new' discovery. An early reference, and possibly the first discoverer, is Ernst von Haselberg (1887). Proof of normal magic hexagons The numbers in the hexagon are consecutive, and run from 1 to 3n^2-3n+1. He ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexagonal Tortoise Problem
The hexagonal tortoise problem () was invented by Korean aristocrat and mathematician Choi Seok-jeong (1646–1715). It is a mathematical problem that involves a hexagonal lattice, like the hexagonal pattern on some tortoises' shells, to the (''N'') vertices of which must be assigned integers (from 1 to ''N'') in such a way that the sum of all integers at the vertices of each hexagon is the same. The problem has apparent similarities to a magic square In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number ... although it is a vertex-magic format rather than an edge-magic form or the more typical rows-of-cells form. His book, ''Gusuryak'', contains many mathematical discoveries. References Sources used * Recreational mathematics Magic shapes {{numtheory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parity (mathematics)
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not.. For example, −4, 0, 82 are even because \begin -2 \cdot 2 &= -4 \\ 0 \cdot 2 &= 0 \\ 41 \cdot 2 &= 82 \end By contrast, −3, 5, 7, 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201. See the section "Higher mathematics" below for some extensions of the notion of parity to a larger class of "numbers" or in other more general settings. Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
